A125248 - OEIS

%I #29 Sep 08 2022 08:45:28

%S 17,38,92,170,248,752,988,2528,8648,12008,34688,63248,117808,526688,

%T 531968,820808,1292768,1495688,2095208,2112512,3477608,4495808,

%U 8419328,12026888,13192768,16102808,26347688,29322008,33653888,169371008

%N Numbers n whose abundance sigma(n)-2n = -16. Numbers n whose deficiency is 16.

%C When p=2^k+15 is prime (cf. A057197), then 2^(k-1)*p is in this sequence. The terms { 17, 38, 92, 248, 752, 2528, 34688, 531968, 2112512, 8419328, 537116672, 2147975168, ...} are of this from, with k in {1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, ...} = A057197. - _M. F. Hasler_, Jul 18 2016

%C Any term x of this sequence can be combined with any term y of A141547 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - _Timothy L. Tiffin_, Sep 13 2016

%H Donovan Johnson, Giovanni Resta and Hiroaki Yamanouchi, <a href="/A125248/b125248.txt">Table of n, a(n) for n = 1..69</a> (terms <= 10^18, first 43 terms from _Donovan Johnson_ and a(44)-a(51) from _Giovanni Resta_)

%e The abundance of 38 = (1+2+19+38)-76 = -16

%t Select[Range[1, 10^6], DivisorSigma[1, #] - 2 # == - 16 &] (* _Vincenzo Librandi_, Sep 14 2016 *)

%o (PARI) for(n=1,1000000,if(((sigma(n)-2*n)==-16),print1(n,",")))

%o (Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -16]; // _Vincenzo Librandi_, Sep 14 2016

%Y Cf. A000203, A033880, A005100; A191363 (deficiency 2), A125246 (deficiency 4), A141548 (deficiency 6), A125247 (deficiency 8), A101223 (deficiency 10), A141549 (deficiency 12), A141550 (deficiency 14), A125248 (this), A223608 (deficiency 18), A223607 (deficiency 20); A141547 (abundance 16).

%K easy,nonn

%O 1,1

%A _Jason G. Wurtzel_, Nov 25 2006

%E a(17) to a(30) from _Klaus Brockhaus_, Nov 29 2006